A NEURAL NETWORK MODEL FOR BANKRUPTCY PREDICTION
Marcus
D.
Odom
Department
of
Accounting
Oklahoma State University
Stillwater, Oklahoma
74078
Ramesh Sharda
College
of
Business Administration
Oklahoma State University
Stillwater, Oklahoma
74078
email:
MGMTRSff@OSUCC.BITNET
ABSTRACT
One interesting area for the use of neural networks is in event prediction.
This study
develops
a
neural network model for prediction of bankruptcy and tests it using financial data from
various companies. The same set
of
data is analyzed
using
a
more traditional method of
bankruptcy prediction, multivariate discriminant analysis. A comparison of the predictive abilities
of
both the neural network and the discriminant analysis method is presented. The results show
that neural networks might be applicable to this problem.
I. INTRODUCTION
Neural networks have proven to be good at solving many tasks. They may have the most
practical effect
in
the following three areas: modeling and forecasting, signal processing,
and
expert
systems [Lippmann, 19871. The predictive ability of neural networks falls into the forecasting
area. Predictive type problems relate to the auto associative memory
of
certain neural networks.
The method used for neural network prediction is called generalization [Dutta and Shekhar, 19891.
Generalization is different from auto associative memory, in that once the network has been
trained, new data is input for the network to predict the output. Previous business applications
of
neural networks include predicting the ratings of corporate bonds [Dutta and Shekhar, 19891, and
emulating mortgage underwriting judgments [Collins, et. al., 19891.
The purpose of this study is to compare the predictive ability of
a
neural network
and
multivariate discriminant analysis models in bankruptcy risk prediction. This area has been studied
extensively in accounting literature. The first studies were performed to determine whether
financial ratios provide useful information [Beaver, 1966; Altman, 19681. Many different studies
have used financial ratios for bankruptcy prediction since that first study by Beaver 1119661. The
majority of these later studies use
a
discriminant analysis approach instead of the univariate
approach used by Beaver. Studies which applied
discriminant analysis include Altman
[
19681,
Deakin [1972], Blum [1974], Moyer [1977], Altman, et.
al.
[1977], and Karels and Prakash [1987].
Discriminant analysis
is
valid only under certain restrictive assumptions, including the requirement
for
the discriminating variables to be jointly multivariate normal. This multivariate normality
of
the variables is critical to the discriminant analysis procedure, otherwise, the results obtained may
be erroneous [Karel and Prakash, 19871. Neural networks are not subject to the restriction of
normality.
A
comparison of a neural network model and a discriminant analysis model, in
bankruptcy prediction, is worthwhile in that we will be able
to
compare a new, more robust
approach against an established method that makes a priori zsumptions about the discriminatory
variables,
The importance of failure analysis provides another motivation for this study. Failure analysis
using financial ratios is very important for several reasons. First, management can use
it
to
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identify potential problems that need attention [Siegel, 19811. Second, investors use ratios to
evaluate
a
firm.
Last, auditors use it
as
a
tool in going-concern evaluation [Altman, 19821. The
American Accounting Association, in A Statement of Basic Accounting Theory, defines accounting
as
"the process of identifying, measuring, and communicating economic information to permit
informed judgments and decisions by users of the information." [1966, p. 11 Rdtio analysis is just
one means of using accounting data for this purpose. This study will see if neural networks are
better predictors of business performance when these same ratios are presented to them.
The approach taken in this study is discussed in the next section. Section 3 is divided into
two parts a discussion of the discriminant analysis model and
a
description of training the neural
network model. Section 4 compares the results of the multivariate discriminant analysis model
with the results of the neural network model. This is followed by the conclusions of the study
and some comments on future studies that may be conducted using neural network models.
11.
METHODOLOGY
The purpose of this study is to perform analysis
on
ratios using both discriminant analysis
and a neural network. The Altman [1968] study is used
as
the standard for comparison for
subsequent bankruptcy classification studies using discriminant analysis. For this reason, we have
chosen to use the same financial ratios that Altman used in his 1968 study. These ratios are:
X1 Working Capital/Total Assets
X2 Retained Earningsnotal Assets
X3 Earnings before Interest and TaxesDotal Assets
X4 Market Value of EquityDotal Debt
X5 SalesDotal Assets
The sample of firms from which the ratios were obtained consisted of firms that went
bankrupt between 1975 and 1982. The sample, obtained from Moody's Industrial Manuals,
consisted of
a
total of 129 firms, 65 of which went bankrupt during the period and 64 nonbankrupt
fms
matched on industry and year. Two subsamples were developed from this sample of 129
fms.
The fist (training) subsample of 74 firms data (38 bankrupt firms and 36 nonbankrupt
fms)
was used
as
the training set for both methods. The second subsample consisted of
55
firms
(27 bankrupt firms and 28 nonbankrupt firms) and
was
used
as
the holdout sample. Data used
for the bankrupt firms is from the last financial statements issued before the firms declared
bankruptcy.
Ratios computed from the data for each original subsample were entered into both a
conventional discriminant analysis program and
a
neural network. The models derived
from
this
original subsample were used to predict the classification for both the training subsample and the
holdout subsample.
111. MODELS FOR BANKRUPTCY PREDICTION
Discriminant Analysis
The multivariate statistical technique known as discriminant analysis is by far the most widely
used method for bankruptcy risk analysis. The program used in this study was SAS DISCRIM
available on the university mainframe computer.
The discriminant analysis method correctly classified 33 of the 38 bankrupt firms for
a
correct
classification rate of 86.84% when using the training subsample. The model correctly classified
all
of the nonbankrupt firms in the training subsample. While this looks promising, the
classification results are based on the same data that was used in model formulation. Therefore,
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caution should be exercised in assessing the validity of the model at this point.
Neural Network
The neural network used for training was
a
three perceptron network consisting
of
an input
layer, a hidden layer, and
the
output layer.
The input layer consisted of the five nodes, one for
each of the ratios. The hidden layer consisted of
5
node.;.
The output layer consisted of only one
neuron with a response of
0,
representing bankrupt,
and
1
,
representing nonbanlmpt. Tlic network
was presented with the ratios for the firms. The network classified the data on
a
scale between
0
and
1.
Firms
with output below
.5
were classified as bankrupt.
Firms with output greater than
.5
were classified
as
nonbankrupt.
Figure
1
x1
x2
x3
x4
x5
>
.5
Nonbankrupt
Bankrupt
The neural network was trained by presenting the five ratios for each of the firms
in
the first
subsample and the correct output for each to the network. The learning threshold for the network
was .075. The initial learning rate and momentum were .6 and .9, respectively. The learning rate
and momentum were adjusted downward
as
suggested by Lippmann
[1987,
p.
181
to improve
performance during training. The learning rate and momentum at the time of convergence were
.1
and
.8
respectively.
One problem with the backpropagation rule,
as
explained in Caudill
[1988,
p.
581,
is
the
number of iterations needed to learn the data. This criticism. held true
in
this project.
Convergence was reached after 191,400 iterations. All of the training was performed on PC-XT.
The average time for training was approximately 24 hours. The software used was Neuroshell,
release
1.1,
a commercial neural network simulator package available for the micro computer from
Ward System Group, Inc.
This program uses
a
backpropagation rule neural network. For more
in depth description of the backpropagation rule refer to Lippmann [1987, pp. 13-18] and
Rummelhart, et. al. [1986, pp. 318-3621.
The neural network correctly predicted all 36
of
the nonbankrupt firms in the training
subsample
as
nonbankrupt.
The trained network also correctly predicted all 38 of the bankrupt
fiis
as
bankrupt. This was very promising when compared to the discriminant analysis prediction
rates for the training subsample.
IV.
COMPARISON
OF'
RESULTS
The results of the multivariate discriminant analysis method and the neural network
are
presented in Table
1
for the holdout sample only. An analysis of the incorrect classifications that
were made by the neural network is presented after explaining Table
1.
In order to test the
robustness of the discriminant analysis model and the neural network, the training sets were
randomly adjusted to be more realistic of the real world ratio of nonbankrupt firms to bankrupt
firms. Three separate groups were formed. The original sample with the
50/50
proportion. The
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second consisted of
36,
(80%),
nonbankrupt
firms
and 9, (20%), bankrupt
firms.
The third group
had 36, (90%), nonbankrupt firms and 4, (lo%), bankrupt firms. These will be referred to
as
the
80/20
and 90/10 training sets.
A
comparison of the results from the models’ predictions for the holdout subsample with the
50/50 training set shows that the discriminant analysis has
a
correct prediction rate of 59.26% for
the bankrupt firms which is well below the correct prediction rate of 81.48% for the neural
network. When the training sample was changed to the 80/20 proportion of non-bankrupt to
bankrupt firms, the discriminant analysis had a correct prediction rate of 70.37% for the bankrupt
fiis
as
compared to the neural network’s correct prediction of 77.78%. When the training sample
was reduced to the 90/10 proportion, the discriminant analysis had a correct prediction rate of
59.26% and the neural network had a correct prediction rate of 77.78% for the holdout subsample.
The neural network appears to be more robust, performing better than the discriminant analysis
method in each of the three situations. The neural network also appears to be more consistent
than the discriminant analysis method.
The discriminant analysis method correctly predicted 89.29% of the nonbankrupt firms while
the neural network predicted 82.14% correctly when trained with the 50/50 sample. Using the
80/20 sample, the discriminant analysis method correctly predicted 85.71%
as
compared to the
neural networks correct prediction rate of 78.57%. However, when the 90/10 sample was used for
training, the neural network did better correctly predicting 85.71% of the holdout subsample, while
the discriminant analysis method predicted only 78.57%.
c
Training Sample Proportion
50/50
80/20 90/10
-
BR
NBR
BR
NBR
Model
Neural
Network
Discrim
Analysis
22
5 21
6 21
6
(81.48) (18.51)
(77.78) (22.22)
(77.78) (22.22)
5
23
6 22
4 24
(17.86) (82.14)
(21.43)
(78.57) (14.29)
(85.71)
16 11 19
8
16 11
(59.26) (40.74) (70.37)
(29.63) (59.26)
(40.74)
3
25
4
24
6 22
(10.71)
(89.29) (14.20)
(85.71) (21.43) (78.57)
BR
=
Bankrupt, NB
=
Nonbankrupt,
%
in
parentheses
Further analysis of the incorrect predictions of the neural network revealed that the five
bankrupt firms that were incorrectly classified as nonbankrupt were also misclassified by the
discriminant analysis model. Of the five nonbankrupt firms
that
were incorrectly classified by the
neural network,
as
bankrupt, three were also misclassified by the discriminant analysis model and
one more was nearly misclassified by this model because it received only
a
51.31% probability
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166
of membership in the nonbankrupt group. These resuIts show that the firms misclassified by the
neural network were also
a
problem for the discriminant analysis method.
It
is more costly to classify
a
failed
fii
as
nonfailed than to classify
a
nonfailed
fii
as
failed [Watts and Zimmerman, 19861. The accountant will be more interested in getting an early
indication of
a
firm
heading towards bankruptcy. Figure
2
exhibits the performance of the two
models in predicting bankruptcy of a firm
as
the training set proportions are varied.
It
clearly
states that regardless of the training sample proportions, the neural network model predicted the
likelihood of
a
firm getting into bankruptcy better.
P
C
e
80
c
'O
OB
ra
--
t
--
n
60
--
e;
1':
I:
$
U
50
--
40
--
r
30
--
I
*O
--
f
10
--
d
a
O--
+
i
-I
Dlscrl.
Ana
Neural
Net
S
50/50
8Oi20
9011
0
Non-bankrupt and
Bankrupt
Firms
In Tralnlng Set
V. CONCLUSIONS
The results obtained from this project show promise in using neural networks for prediction
purposes.
This
research compared neural networks against
a
method that
has
become the "rule"
in bankruptcy prediction, and the neural network performed better on both the original set of data
and on predicting the bankrupt firms in the holdout sample. The neural network proved to be
more robust than the discriminant analysis method on reduced sample sizes.
Further research should be done in this area using different ratios to see
if
the prediction
accuracy can
be
increased. The ratios
in
this study were based on
a
study completed in 1968,
different ratios may perform better today [Altman, et. al., 19771. Another area for future research
may
be
in
applying different neural network architectures to this problem. Comparison
of
these
other architectures may help to identify the best architecture for this type of problem.
VI. REFERENCES
Altman,
E. I.,
"Financial Ratios, Discriminant Analysis and the Prediction of Corporate
Bankruptcy," The Journal of Finance (September 1968), pp. 589-609.
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167
,
Haldeman, R. G. and Narayanan, P., "Zeta Analysis," Journal of Banking and Finance
(June 1977), pp. 29-51.
,
"Accounting Implications of Failure Prediction Models," Journal
of
Accounting Auditing
&
Finance (Fall 1982), pp. 4-19.
,
and Spivack, J., "Predicting Bankruptcy: The Value Line Relative Financial Strength
System vs. the Zeta Bankruptcy Classification Approach," Financial Analysts Joumal
(November-December 1983), pp. 60-67.
American Accounting Association, A STATEMENT OF BASIC ACCOUNTING THEORY (AAA,
1966).
Beaver, W.
H.,
"Financial Ratios
as
Predictors of Failure," Empirical Research in Accounting:
Selected Studies, 1966, pp. 71-1
11.
Belkaoui, A., ACCOUNTING THEORY (Harcourt Brace Jovanovich, Inc., 198 1).
Blum, M., "Failing Company Discriminant Analysis," Journal of Accounting Research (Spring
.
1974), pp. 1-25.
Caudill, M., "Neural Networks Primer, Part III,"
AI
Expert (June 1988), pp. 53-59.
Collins, E., Ghosh,
S.,
and Scofield, C., "An Application of
a
Multiple Neural .Network Learning
System to Emulation
of
Mortgage Underwriting Judgements," Working Paper (Nestor, Inc.,
1
Richmond Square, Providence,
RI,
1989).
Deakin, E. B., "A Discriminant Analysis
of
Predictors
of
Business Failure," Joumal
of
Accounting
Research (Spring 1972), pp. 167-179.
Dutta,
S.
and Shekhar,
S.,
"Bond Rating: A Non-Conservative Application of Neural Networks,"
Working Paper (Computer Science Division, University
of
California, 1989).
Karels, G. V. and Prakash, A., "Multivariate Normality and
Forecasting
of
Business Bankruptcy,"
Journal
of
Business Finance
&
Accounting (Winter 1987), pp. 573-93.
Lippmann,
R.
P., "An Introduction to Computing with Neural Nets," IEEE ASSP Magazine (April
1987),
pp.
4-22.
Moyer, R. C., "Forecasting Financial Failure: A Reexamination," Financial Management (Spring
1977),
pp.
11-17.
Rumelhart, D.
E.,
Hinton, G. E., and Williams,
R.
J., "Learning Internal Representation by Error
Propagation," Parallel Distributed Processing, Vol. 1 (Cambridge, MA: MIT Press 1986).
Siegel,
J.
G.,
"Warning Signs
of
Impending Business Failure and Means to Counteract such
Prospective Failure," The National Public Accountant (April 198l), pp. 9-13.
Watts, R.
L.
and Zimmerman, J. L., POSITIVE ACCOUNTING THEORY (Prentice-Hall, Inc.,
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